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Mathematics Cheat Sheet [pdf] (keybase.pub)
225 points by weatherlight 10 days ago | hide | past | favorite | 67 comments

In Bulgaria there is a little yellow book that carries all the rules in mathematics one would need through all of K-12 and then some. It has quadratic formulas, limits, trigonometry (including sin/cos conversion tables), not as many physics formulas though. Everything is explained succinctly as well. It is a commonly used and required book in all schools and it gives you a quick review of anything you need before math competitions, tests, or just brush up after a while. There absolutely needs to be a book like that for US kids and the baseline math levels here will rise up substantially.

The small yellow book might have already fallen out of fashion. I graduated from a math high school in Bulgaria about 10 years ago, and I vaguely remember the yellow book being referred to as if it was popular during the stone age.

Is it available in english? Or any other equivalent book in english?

It's not really comparable to the yellow book and its meant as a glossary for an older audience, but I've found Mathematical Notation: A Guide for Engineers and Scientists [1] to be useful, especially for reading CS and ML papers.

[1] https://www.amazon.com/Mathematical-Notation-Guide-Engineers...

The Art of Problem Solving series has this. The Basics, Vol. 1, and Beyond, Vol. 2, are a lot like that. They aren't course material. AOPS has that with Prealgebra thru Calculus. These are distillations for contest math with explanations and problems.

Is it in Cyrillic or Latin ? Do you know if its available online ?

It's in Cyrillic. The official title is "Четиризначни математически таблици и формули".

googled Четиризначни because didn't recognize it as a russian word (it means four digit) and the first hit is that book


Bulgarian is a distinct language using the Cyrillic alphabet (as is for instance Macedonian, Serbian and Ukrainian)

wikipedia used to have this


e.g. i understood the other two words in the title no problem.


i'm from moldova and i speak russian and understand ukrainian pretty easily. calling them distinct languages is true but it's pedantic - it's a very blurry line how mutually intelligible the two languages are.

-Similar story where I come from - Norwegian, Swedish and Danish are sufficiently similar that we can mostly understand each other without much effort, especially (my opinion) in writing - Danish pronunciation is far more challenging to grasp than Swedish, at least to my Norwegian ears.

It's not Russian language. Close, but it's not.

This came up 2 years ago on Hacker News[1] and I wrote the following:


I think the author's page (Alex Spartalis) deserves to be mentioned:


He has the same version (v2.10) there and mentions that, "The Web version does not include the distribution functions due to file size restrictions. Email me if you would like a copy of these." That explains why pages 213-330 are missing. Someone should offer to upload the full copy to keybase.pub (or someplace) since his personal site can't handle the load.

People sometimes do tremendous work creating a program/book/artwork, and want the world to see it, but don't get around to really share it or promote it.


However, now it appears that Alex's site no longer exists and nobody (including me) ever did upload the full copy to keybase.pub.

[1] https://news.ycombinator.com/item?id=20048205

Also, here is backup of Alexander Spartalis' 640-pages "The Mathematics Handbook", v4.1, June 2nd, 2019.[0,1,2]

> However, now it appears that Alex's site no longer exists

In 2019 Alex moved to new site, which also is not availabale anymore, BUT there are backups of both sites.[0,3]

JFTR, You may try contact with Alex Spartails via Facebook & Instagram.[4,5]

[0] http://web.archive.org/web/20200127012510/http://mathscheats...

[1] https://drive.google.com/file/d/1MM2Hu5qlptkg8dNLM9QibeXHErL...

[2] https://www.scribd.com/document/412167295/the-mathematics-ha...

[3] http://web.archive.org/web/20190530065518/https://www.alexsp...

[4] https://m.facebook.com/alexspartails

[5] https://instagram.com/alexspartails

That is "The Mathematics Handbook", v4.1

I meant his website.

> his website

Since 2018 sites hosted on Weebly not available in many countries due to Weebly's self-censorship.[0]

[0] https://en.wikipedia.org/wiki/Weebly#Censorship

Do people really use this or any other of the cheatsheets you find online?

In my experience, any cheat sheet that I didn't make myself is useless to me. Going directly to the sheet without having done the synthesis of information yourself skips the most important part of the process.

Yes, you make your own sheets of the things you can never quite remember.

Often going through that process leaves you remembering them.

These cheetsheets aren't meant to be printed off and carried into your open book tests. They are meant to be greppable formula lookups. They're useful if you can define the problem but don't know the equation off your head to solve it. Think something like differentiating a trig function after you haven't used it in a while or looking up some statistical approximation.

I do. Mainly for things I don't really intend to memorize. It's just an easier reference than, say, a man page.

Pretty much anything is easier to reference than a man page :) I wish the standard for man, would be to include examples. But maybe I'm in the minority of people who learn by example.

> would be to include examples

strongly agree. Some do but not all, so you can't rely on it. Those tldr sites are reasonable alternatives for most commands.

They tend to be a great resource for rarely used knowledge.

The key is remembering you have a cheatsheet for that rarely used knowledge.

Math cheatsheet made by others are not very useful. When it's not about a large public API it doesn't really make sense. People also forget that most theorems/formulas have slight modifications that are very useful but make these kind of enterprise very difficult.

Same for me. I need to start with the bulk of the info and start to compress it to be helpful to me.

My first thought what an outstanding pdf, my second though;

this should be in latex on github/gitlab, so people can contribute and maintain, I would love to add numerical psedo code to as much equations as I possibly can with my primitive comprehension of mathematics.

Let's do this; I just created https://github.com/Accacio/math-cheatsheet, When I get time I will implement CI/CD to genereate the pdfs

> When I get time I will implement CI/CD to genereate the pdfs

You may take a look on `.travis.yml`[0] used for MetaPost + ConTeXt rendition of Oliver Byrne's "The first six books of the Elements of Euclid".[1]

[0] https://github.com/jemmybutton/byrne-euclid/blob/master/.tra...

[1] https://github.com/jemmybutton/byrne-euclid/releases/tag/Cur...

done it differently

But thanks any way

Yeah that was my first thought too. I want the LaTeX so I can re-typeset it.

Might be some copyright issues. I see non-attributed images in the Moments of Inertia section that are licensed CC BY-SA on Wikipedia. Also apparently some text book scans.

In my country every engineering or math student had a copy of a translation of a book by the Russian authors Bronshtein and Semendyayev.


+1 for Bronstein. I had classmates in my physics program who brought their family bronstein (later my father who majored in German philology told me he had a Bronstein himself for when he tried to study civil engineering, but gave it away to a friend after switching majors, I would have loved to have a family Bronstein :-) )

Theoretical Computer Science Cheat Sheet is a more elegant and concise actual math cheat sheet, compared to this handbook.


Nope, for someone who is almost completely ignorant of mathematics and especially tripped up in learning more because they don't know enough mathematical notation, the OP is much better because it actually explains the meaning of various notation symbols. Your link just jumps into formulas full of them without contextualizing these basics.

Would you call a two hundred page document a cheat sheet?

Some interesting constants and series but a lot of Trigonometry, Differentiation and Calculus formulas...More Math than Computer Science I would say.

I noticed that the physical constants might be outdated. As I understand it, the Planck constant is now considered to be a defined quantity.


Indeed. Avogadro's number too now has an exact value and all that stuff that depends on it has changed with it.

Sorry if I sound exclusively negative about someone else's hard work – that is not the intention.

I find people's obsession over memorizing mathematical symbols (part 2) really strange. If you understand what the concepts involved in a symbol mean, you won't have a problem recognizing the commonly used symbols. And if you don't understand what the concepts involved mean, then having memorized the symbol does you no good.

Am I missing something?

Edit, since I'm apparently in a very critical mood today: It seems very strange for a document to barely scratch the absolute essentials for something as important and broadly applicable as linear algebra, yet go on and on and on with quite esoteric lists of special primes that surely concern at most researchers in specialized parts of number theory? Of all the lists of primes that the author chooses to focus on, I must say I had only heard of three (Fibonacci, Mersenne and Gaussian). Granted, my PhD is in a very different part of math, but this seems a bit… crazy… in such a document. (Also, are the lists "even primes: 2", and "odd primes [insert list of all other primes here]" meant as jokes?)

Edit 2: Same goes with the obsession with pi. The amount of effort and space spent on features of primes and pi that are incredibly unimportant except to very specialized researchers is… a bit insane in a document like this.

>If you understand what the concepts involved in a symbol mean, you won't have a problem recognizing the commonly used symbols. >And if you don't understand what the concepts involved mean, then having memorized the symbol does you no good.

this would imply in learning a new language if you know what the concepts a word refers to means that you won't have any difficulty recognizing the word - no matter how many words there are, how long the statement you are reading is, and how similar various words are to each other?

When learning something it is nice to have a reference.

Indeed - formal symbols have no intrinsic meaning, and one must learn their meaning as a separate step from learning their form and how to recognize them.

One's chances of finding out what an unfamiliar symbol means in context (or a familiar symbol in unfamiliar usage) is greatly helped (though not completed) if you can get a name or one or more précis of its uses.

If it is about memorizing then yeah, I don't get it. If it is a handy reference for I found a weird symbol what does it mean, then I do. When I was 14, I found a 1960s era electrical engineering text book. Being rather nerdy I bought it and read most of it. The only problem was I didn't understand the math because it had this weird S symbol in it. I didn't know what it was called or what it was about so I couldn't even formulate the question to find out more.

I don't think this is supposed to be a serious attempt to write a math reference book, this looks much more like the result of personal interests. That would very well explain why a lot of room is allocated to niche topics while on the other hand entire areas areas of mathematics are missing.

I immediately went to save this file to my collection of ebooks/pdfs. I have the same file from mid 2019 apparently!

Going by the dates in the file and the listed values of the physical constants it also hasn't been updated in a while.

Typo on page 56, "Laprange" instead of "Lagrange". Also I find it strange that logarithms are part 10 / page 121, after Newtonian mechanics.



This site might have an alternative copy that's been updated more recently: http://mathscheats.weebly.com/2019-downloads.html

I still wish there was LaTeX for it.

> I still wish there was LaTeX for it.

As email probably unavailable, there are Alex's Facebook/Instagram.[0]

[0] https://news.ycombinator.com/item?id=27468908#27469861

Well, this[0] takes the cake for the way Maths is promoted on that website :)

Stumbled upon the website while searching for the complete version of the OP link.

[0] http://nanar.com

Eddie Shore's blog has a true cheat sheet sized "Big Font Math Reference".


This is awesome, I use evince and okular to open the pdf and could not find the table-of-content on the left side of the pdf readers, which is an essential feature for PDFs, can the PDF re-generated to produce that?

Probably the best applied math "tutorial" without all the bullshit I've yet seen is the mathematical background appendix in Probabilistic Machine Learning: An Introduction by Kevin P. Murphy.

What is this useful for, page 45?

Rational Numbers: Every rational number can be written as r = [(r - 1) + (r + 1)] / 2

I would have expected p / q with p and q integers or some variation of this.

That is indeed strange. And why restrict it to rationals, when it's true for every real (or every complex, whatever)? It's even true for integers, under a suitable interpretation of what is meant by dividing by 2 in that case.

It's also totally trivial when you rewrite it slightly: (r + r + 1 - 1) / 2. So basically adding r to itself to get 2r then dividing by 2 gives you back r, with a pointless plus and minus 1 thrown in.

It's trivial only if you are simplifying mathematical expression.

When you have to go the opposite direction, you start with r and must turn it something that fits some other expression, there are infinite ways to proceed. Right ones rarely just pop up into your mind.

Remembering trivial identities things like that are useful as small intermediate steps when manipulating expressions.

But this still does not answer why this expression is specifically listed for rational numbers as it is true for subsets of the rational numbers like the integers as well as for supersets of the rational numbers like the real numbers.

Wait, what? Is this a rendering bug, or a typo?

> γ = 0.527721566...

I think it's closer to 0.577 215 664 901 ... see https://en.wikipedia.org/wiki/Euler%E2%80%93Mascheroni_const...

Reminds me of the Schaum’s Outline Mathematical Handbook of Formulas and Tables by Murray Spiegel, which is more concise and better organized. My uncle gave me his copy when I was 12 years old and that got me started on my road to mathematics.

That's pretty great! Notation and shorthand seems to trip even the most capable mathematicians up. I remember making these all the time as a student to try an help. The probability section might be the most important IMO.

That’s quite a cheat sheet. Thank you.

Wow. What a treasure trove Thanks for posting!

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